Question

the graph shows the motion of a mouse. mouses position vs. time. at what time does the mouse get back to where he started? 30s. at t = 10s, how far has the mouse moved? 30m. what is the slope of the line from t = 25s to t = 35s? what information does the slope this line tell you about the mouse?

Explanation:

Step1: Recall slope - velocity relation

In a position - time graph, the slope of the line represents the velocity of the object.

Step2: Find the slope from t = 25s to t = 35s

The position at t = 25s is 0m and at t = 35s is 30m. Using the slope formula $m=\frac{\Delta y}{\Delta x}=\frac{x_2 - x_1}{t_2 - t_1}$, where $x_1 = 0m$, $x_2=30m$, $t_1 = 25s$, $t_2 = 35s$. So $m=\frac{30 - 0}{35 - 25}=\frac{30}{10}=3m/s$. The positive slope means the mouse is moving in the positive direction.

Step3: Determine distance moved at t = 10s

At t = 0s, the position is 40m and at t = 10s, the position is 10m. The distance moved $\Delta x=40 - 10 = 30m$.

Step4: Find time to return to starting - point

The mouse starts at 40m. It moves to 0m and then back to 40m. Looking at the graph, it returns to the starting - point at t = 30s.

Step5: Interpret slope information

The slope of the line tells us the velocity of the mouse. A positive slope means the mouse is moving in the positive direction (away from the origin in the position - axis), a negative slope means it is moving in the negative direction (towards the origin in the position - axis), and a zero slope means it is at rest.

Answer:

• The slope from t = 25s to t = 35s is 3m/s.
• At t = 10s, the mouse has moved 30m.
• The mouse gets back to where it started at 30s.
• The slope of the line tells us the velocity of the mouse.